Budget allocation problems in portfolio management are inherently multi-objective as they entail different types of assets of which performance metrics are not directly comparable. Existing asset management methods that either consolidate multiple goals to form a single objective (a priori) or populate a Pareto optimal set (a posteriori) may not be sufficient because a decision maker (DM) may not possess comprehensive knowledge of the problem domain. Moreover, current techniques often present a Pareto optimal set with too many options, making it counter-productive. In order to provide the DM with a diverse yet compact solution set, this paper proposes a three-step approach. In the first step, we employ different approximation functions to capture investment-performance relationships at the asset-type level. These simplified relationships are then used as inputs for the multi-objective optimisation model in the second step. In the final step, Pareto optimal solutions generated by a selected evolutionary algorithm are pruned by a clustering method. To measure the spread of representative solutions over the Pareto front, we present two novel indicators based on average Euclidean distance and cosine similarity between original Pareto solutions and representative solutions. Through numerical examples, we demonstrate that this approach can provide a set of representative solutions that maintain high integrity of the original Pareto front. We also put forward suggestions on choosing appropriate approximation functions, pruning methods, and indicators.

投资组合管理中的预算分配问题本质上是多目标的，因为它们涉及不同类型的资产，其绩效指标不能直接比较。现有的资产管理方法要么合并多个目标以形成单个目标（先验）或填充帕累托最优集（后验）) 可能还不够，因为决策者 (DM) 可能不具备问题领域的全面知识。此外，当前的技术通常会呈现具有太多选项的帕累托最优集，从而适得其反。为了向 DM 提供多样化但紧凑的解决方案集，本文提出了一个三步法。第一步，我们采用不同的近似函数来捕捉资产类型级别的投资绩效关系。然后将这些简化的关系用作第二步中多目标优化模型的输入。在最后一步，由选定的进化算法生成的帕累托最优解通过聚类方法进行修剪。为了衡量代表性解决方案在帕累托前沿的传播，我们基于原始帕累托解决方案和代表性解决方案之间的平均欧几里德距离和余弦相似度提出了两个新指标。通过数值例子，我们证明这种方法可以提供一组具有代表性的解决方案，保持原始帕累托前沿的高度完整性。我们还就选择合适的近似函数、剪枝方法和指标提出了建议。